2 papers
math.NA2025
A Variational Physics-Informed Neural Network Framework Using Petrov-Galerkin Method for Solving Singularly Perturbed Boundary Value Problems
Vijay Kumar, Gautam Singh
This work proposes a Variational Physics-Informed Neural Network (VPINN) framework that integrates the Petrov-Galerkin formulation with deep neural networks (DNNs) for solving one-…
math.NA2025
Development and Analysis of Chien-Physics-Informed Neural Networks for Singular Perturbation Problems
Gautam Singh, Sofia Haider
In this article, we employ Chien-Physics Informed Neural Networks (C-PINNs) to obtain solutions for singularly perturbed convection-diffusion equations, reaction-diffusion equation…